Geometry

Volume and surface area

Solid geometry asks for volume, surface area or a missing length. Answers are often given as a multiple of π, so keep π as a symbol until the end.

The rules

• Prism and cylinder: V = base area · height; cylinder V = πr²h.
• Pyramid and cone: V = ⅓ · base area · height; cone V = ⅓πr²h.
• Sphere: V = ⁴⁄₃πr³, surface O = 4πr².
• Volume units step by 1000: 1 m³ = 1000 dm³ = 1000 litres.

Practice questions with solutions

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. 1. A rectangular box measures 3 × 5 × 2. What is its volume?

   • a30
   • b62
   • c33
   • d10
   Show solution

   Answer: 30

   Volume of a box = length · width · height.

   3 · 5 · 2 = 30.

2. 2. A rectangular box measures 6 × 6 × 5. What is its volume?

   • a192
   • b186
   • c180
   • d17
   Show solution

   Answer: 180

   Volume of a box = length · width · height.

   6 · 6 · 5 = 180.

3. 3. A rectangular box measures 5 × 5 × 6. What is its volume?

   • a16
   • b150
   • c155
   • d170
   Show solution

   Answer: 150

   Volume of a box = length · width · height.

   5 · 5 · 6 = 150.

4. 4. Convert: 3.2 l = ? cm³

   • a32000
   • b3200
   • c32
   • d0.0032
   Show solution

   Answer: 3200

   1 l = 1 dm³ = 1000 cm³ = 1000 ml, and 1 m³ = 1000 l: for volumes the length factor counts three times.

   1 l = 1000 cm³, so 3.2 l = 3.2 · 1000 = 3200 cm³.

5. 5. A rectangular box measures 6 × 2 × 2. What is its volume?

   • a24
   • b56
   • c10
   • d30
   Show solution

   Answer: 24

   Volume of a box = length · width · height.

   6 · 2 · 2 = 24.

6. 6. A rectangular box measures 6 × 4 × 2. What is its volume?

   • a54
   • b48
   • c88
   • d12
   Show solution

   Answer: 48

   Volume of a box = length · width · height.

   6 · 4 · 2 = 48.

Common mistakes

• Forgetting the ⅓ for pyramids and cones.
• Converting volume units by 10 or 100 instead of 1000.
• Using the diameter as the radius.

Related topics

All maths topics · T-Kurs · M-Kurs · W-Kurs